Block LU factorizations of M-matrices

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 1998Embargo end date: 01 Mar 1998Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 80, pages 109-130 (issn: 0029-599X, eissn: 0945-3245,

Copyright policy )Funded by:NSERC | unidentified, NSF | Mathematical Sciences: Ma..., NSF | Mathematical Sciences: Ma...

Authors: Judith J. McDonald; Hans Schneider;

doi: 10.1007/s002110050362 , 10.48550/arxiv.math/9803098

arXiv: math/9803098

Block LU factorizations of M-matrices

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Abstract

It is well known that any nonsingular M-matrix admits an LU factorization into M-matrices (with L and U lower and upper triangular respectively) and any singular M-matrix is permutation similar to an M-matrix which admits an LU factorization into M-matrices. Varga and Cai establish necessary and sufficient conditions for a singular M-matrix (without permutation) to allow an LU factorization with L nonsingular. We generalize these results in two directions. First, we find necessary and sufficient conditions for the existence of an LU factorization of a singular M-matrix where L and U are both permitted to be singular. Second, we establish the minimal block structure that a block LU factorization of a singular M-matrix can have when L and U are M-matrices.

Related Organizations

University of Wisconsin–Oshkosh
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University of Regina
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UNIVERSITY OF WISCONSIN-MADISON
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University of Wisconsin–Madison
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Keywords

Rings and Algebras (math.RA), LU factorization, FOS: Mathematics, Mathematics - Combinatorics, Mathematics - Rings and Algebras, Combinatorics (math.CO), M-matrix, Direct numerical methods for linear systems and matrix inversion, block matrix, Factorization of matrices

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